// Numbas version: exam_results_page_options
{"name": "Indefinite integration using standard integrals", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "\n  <p>Integrate the following function $f(x)$.</p>\n  <p><br/>You must input the constant of integration as $C$.</p>\n  ", "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "s3", "s2", "s1", "s5", "s4", "a1", "a2", "b1", "c3"], "metadata": {"description": "<p>Integrate $f(x) = ae ^ {bx} + c\\sin(dx) + px^q$. Must input $C$ as the constant of integration.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variable_groups": [], "preamble": {"js": "", "css": ""}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "name": "Indefinite integration using standard integrals", "tags": [], "advice": "\n  <p>Splitting the integral into three parts and using the information in Steps we have:&nbsp;</p>\n  <p>\\[\\begin{eqnarray*}\\simplify[std]{Int({b} * e ^ ({a}*x) + {b1} * Sin({a1}*x) + {a2} * x ^ {c3},x)}&amp;=&amp;\\simplify[std]{Int({b} * e ^ ({a}*x),x)+Int({b1} * Sin({a1}*x),x)+Int({a2} * x ^ {c3},x) }\\\\ &amp;=&amp;\\simplify[std]{({b}/{a}) * (e ^({a}*x)) + (({(-b1)}/{a1}) * Cos({a1}*x)) + ({a2}/{c3+1}) * (x ^ {(c3 + 1)})+C} \\end{eqnarray*}\\]</p>\n  ", "parts": [{"stepsPenalty": 0, "adaptiveMarkingPenalty": 0, "scripts": {}, "variableReplacements": [], "marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": [], "prompt": "\n      <p>$\\simplify[std]{f(x) = {b} * e ^ ({a}*x) + {b1} * Sin({a1}*x) + {a2} * x ^ {c3}}$</p>\n      <p>$\\displaystyle \\int\\;f(x)\\,dx=\\;$[[0]]</p>\n      <p>Enter all numbers as integers or fractions and not as decimals.</p>\n      ", "sortAnswers": false, "showFeedbackIcon": true, "gaps": [{"adaptiveMarkingPenalty": 0, "variableReplacements": [], "marks": 3, "useCustomName": false, "answerSimplification": "std", "notallowed": {"partialCredit": 0, "message": "<p>Enter all numbers as integers or fractions and not as decimals.</p>", "showStrings": false, "strings": ["."]}, "customMarkingAlgorithm": "", "unitTests": [], "vsetRange": [0, 1], "showCorrectAnswer": true, "vsetRangePoints": 5, "failureRate": 1, "variableReplacementStrategy": "originalfirst", "type": "jme", "scripts": {}, "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "checkingType": "absdiff", "answer": "({b}/{a}) * e ^({a}*x) + (({(-b1)}/{a1}) * Cos({a1}*x)) + ({a2}/{c3+1}) * (x ^ {(c3 + 1)})+C", "showPreview": true, "showFeedbackIcon": true, "valuegenerators": [{"value": "", "name": "c"}, {"value": "", "name": "x"}], "customName": ""}], "showCorrectAnswer": true, "customName": "", "type": "gapfill", "steps": [{"adaptiveMarkingPenalty": 0, "scripts": {}, "variableReplacements": [], "marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": [], "prompt": "<p>Note that \\[\\begin{eqnarray*} &amp;\\int&amp; \\;x^n\\;dx&amp;=&amp;\\frac{x^{n+1}}{n+1}+C,\\;\\;n \\neq -1\\\\ &amp;\\int&amp; \\;\\sin(ax)\\;dx &amp;=&amp; -\\frac{1}{a}\\cos(ax)+C\\\\ &amp;\\int&amp; \\;e^{ax}\\;dx &amp;=&amp; \\frac{1}{a}e^{ax}+C\\\\ \\end{eqnarray*}\\]</p>", "showFeedbackIcon": true, "showCorrectAnswer": true, "customName": "", "type": "information", "variableReplacementStrategy": "originalfirst"}], "variableReplacementStrategy": "originalfirst"}], "functions": {}, "extensions": [], "variables": {"b": {"definition": "s2*random(2..9)", "group": "Ungrouped variables", "name": "b", "templateType": "anything", "description": ""}, "c3": {"definition": "s5*random(2..8)", "group": "Ungrouped variables", "name": "c3", "templateType": "anything", "description": ""}, "s3": {"definition": "random(1,-1)", "group": "Ungrouped variables", "name": "s3", "templateType": "anything", "description": ""}, "a1": {"definition": "random(2..5)", "group": "Ungrouped variables", "name": "a1", "templateType": "anything", "description": ""}, "a": {"definition": "s1*random(2..5)", "group": "Ungrouped variables", "name": "a", "templateType": "anything", "description": ""}, "b1": {"definition": "s3*random(2..9)", "group": "Ungrouped variables", "name": "b1", "templateType": "anything", "description": ""}, "s1": {"definition": "random(1,-1)", "group": "Ungrouped variables", "name": "s1", "templateType": "anything", "description": ""}, "s5": {"definition": "random(1,-1)", "group": "Ungrouped variables", "name": "s5", "templateType": "anything", "description": ""}, "s4": {"definition": "random(1,-1)", "group": "Ungrouped variables", "name": "s4", "templateType": "anything", "description": ""}, "a2": {"definition": "s4*random(3..9)", "group": "Ungrouped variables", "name": "a2", "templateType": "anything", "description": ""}, "s2": {"definition": "random(1,-1)", "group": "Ungrouped variables", "name": "s2", "templateType": "anything", "description": ""}}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Thomas Waters", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3649/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Thomas Waters", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3649/"}]}